Use a graphing calculator to write a polynomial function to model this set of data
{(5,2) (7,5) (8,6) (10,4) (11, -1) (12 -3) (15,5) (16,9)}
A) f(x) = 2x3 + 2.70x2 + 0.09x - 65.21
B) f(x) = 2x3 - 0.09x - 65.21
C) f(x) = 0.09x3 - 2.70x2 + 24.63x - 65.21
D) f(x) = x4 - 5.7x3 + 2.70x2 + 24.63x - 65.21
It is a bit difficult to show you such a graph here.
What you want to do is graph those functions in the domain from about (0,-10) to (20,10) and put your discrete points on the graph. Then you can see which function comes close to the points.
for example your first function looks like this
http://www.wolframalpha.com/input/?i=2x3+%2B+2.70x2+%2B+0.09x+-+65.21+%2C+x%3D-10+to+%2B10
it seems for example you do not want 2 x^3 in there because it is huge for x = 15 for example. so A and B are questionable and D does not look so hot either.
To find the polynomial function that models the given set of data, we can use a graphing calculator.
1. Enter the given data points into the calculator.
2. Go to the graphing mode of the calculator.
3. Plot the points on the graph.
4. Use the calculator's tools or functions to find the best-fit curve that passes through these points.
5. Based on the curve that best fits the data points, determine the equation of the polynomial function.
Looking at the given options:
A) f(x) = 2x^3 + 2.70x^2 + 0.09x - 65.21
B) f(x) = 2x^3 - 0.09x - 65.21
C) f(x) = 0.09x^3 - 2.70x^2 + 24.63x - 65.21
D) f(x) = x^4 - 5.7x^3 + 2.70x^2 + 24.63x - 65.21
Using the graphing calculator, plot the points {(5,2) (7,5) (8,6) (10,4) (11, -1) (12, -3) (15,5) (16,9)} and look at the best-fit curve. Check which of the given options match the curve on the graph.
After following these steps, the best-fit curve should closely match the points. Based on the curve that fits the data, the correct answer will be the option that matches the equation of the curve. Choose the option accordingly.
Note: The specific graphing calculator may have different functions or steps, so refer to the calculator's user manual or instructions for precise guidance.